Minimising costs at Petfoodies Inc.

Petfoodies Inc. produces animal food, which is delivered in packs of 10 kg each. For the production of pet food, the company mixes three different ingredients, namely Corn, Seeds and Additives. The costs of these ingredients are €0.40, €0.60 and €0.80 per kilogram respectively.

Government regulation prescribes that each kilogram of pet food should contain at least 30%

corn, 30% seeds and 10% additives. Additionally, each kilogram of pet food should have at least 400 Kcal in nutrition value. We know that each kilogram of corn or seed adds 400 Kcal, and each kilogram of additive adds 600 Kcal nutrition value to pet food.

For next month, the market asks for 1 00 000 Kg pet food, which comes down to the production of 10 000 packs of 10 Kg pet food. The price levels of ingredients on the market fluctuate considerably over time and Petfoodies wants to minimise costs as much as possible.

Required:

1. How much of each ingredient should Petfoodies buy on the market to produce the 10 000 packs of pet food required, under the condition of cost minimisation and adherence to government regulations?

2. Suppose the association of pet food producers offers to lobby for relaxing the composition and product quality constraints, which constraint would then be your favourite if your primary goal is to minimise costs?

3. The cost price of corn has risen to €0.70 eurocents per kilogram. Does this change the solution of the LP-model? How can you predict this?